A simple algorithm, based on recursive quadratic optimization, is suggested for the numerical inversion of integral transforms. The algorithm was found particularly useful for “small scale” problems, with the number of independent parameters ranging between 100 and 200. The programming, parameterization, and performance of the algorithm are discussed, as well its application to the analysis of time-resolved luminescence data.
McWhirterJ. G. and PikeE. R, J Phys. A: Math. Gen, 11, 1729 (1978).
2.
See, for example, WareR. in Photochemistry in Organized and Constrained Media, RamamurthyV. Ed. (VCH Publishers, New York, 1991), p. 563 and references therein.
3.
IstratovA. A. and VyvenkoO. F, Rev. Sci. Instr.70, 1233 (1999).
4.
TikhonovA. N., Sov. Math. Dokl.4, 1035 (1963).
5.
TikhonovA. N., Solutions of Ill-Posed Problems (John Willey and Sons, London, 1977).
6.
EnglH. W.HankeM. and NeubauerA, Regularization of Inverse Problems (Kluwer, Dordrecht, 1996).
LandlG.LangthalerT.EnglH. W. and KauffmannH, J. Comp. Phys.95, 1 (1991).
10.
KaufmannH. F.LandlG. and EnglH. W, in Large Scale Molecular Systems—Quantum and Stochastic Aspects: Beyond the Simple Molecular Picture, GansW.BlumenA. and AmannA, Eds. (Plenum, New York, 1991), p. 503.
11.
Historically MEM has appeared independently from the regularization methods. It was analyzed as a regularization technique, for example, in EnglH. W. and LandlG Eds. SIAM J. Num. Anal.30, 1509 (1993).
12.
JanesE. T., Papers on Probability, Statistics and Statistical Physics (Reidel, Dordrecht, 1983).
13.
SkillingJ., in Maximum Entropy and Bayesian Methods, SkillingJ. Ed. (Kluver, Dordrecht, 1989), p. 45.
14.
GullS. F. and SkillingJ, in Indirect Imaging, RobertsJ. A. Ed. (Cambridge University Press, Cambridge, 1984), p. 267.
15.
LiveseyA. K. and BrochonJ. C, Biophys J.52, 693 (1987).
16.
BrochonJ. C., in Numerical Computer Methods, JohnsonM. L. Ed. (Academic Press, San Diego, California, 1994), Vol. 240, p. 262.
17.
SkillingJ. and BryanR. K, Mont. Not. R. Astr. Soc.211, 111 (1984).
18.
CornwellT. J. and EvansK. F, Astron. Astrophys.143, 77 (1985).
19.
VinogradovS. A. and WilsonD. F, Biophys. J.67, 2048 (1994).
20.
ShragerR. I., Comm. ACM15, 41 (1972).
21.
BabushkinskyA. and GoncharskyA, Ill-Posed Problems: Theory and Applications (Kluwer, Dordrecht, 1994).
TikhonovA. N.GoncharskyA. V.StepanovV. V. and YagolaA. G, Numerical Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1990), in Russian.
24.
VinogradovS. A.LoL. W. and WilsonD. F, Chem. Eur. J.5, 1338 (1999).
25.
PressW. H.TeukolskyS. A.VetterlingW. T. and FlannerlyB. P, Numerical Recipes in C. The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992), 2nd ed.
26.
SemiarczukA.WagnerB. D. and WareW. R, J. Phys. Chem.94, 1661 (1990).
27.
ShaverJ. M. and McGownL. B, Anal. Chem.68, 9 (1996); ibid., 68, 611 (1996).